Using Chebyshev Polynomials to Approximate Partial Differential Equations
This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists in determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining the best policy for shutting down a machine. The suggested method is flexible, easy to programme and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.
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Volume (Year): 35 (2010)
Issue (Month): 3 (March)
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- Avinash Dixit, 1992. "Investment and Hysteresis," Journal of Economic Perspectives, American Economic Association, vol. 6(1), pages 107-132, Winter.
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- Elias Tzavalis & Shijun Wang, 2003. "Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary," Working Papers 488, Queen Mary University of London, School of Economics and Finance.
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